Joint models for longitudinally measured outcomes and non-terminal recurrent event processes – developing a framework


Approximately 30% of the United Kingdom population live with at least one long-term or chronic condition such as diabetes or asthma.  Many of these are typified by recurrent events over time, such as exacerbations in asthma, or seizures in epilepsy.  Currently, discussions concerning treatment and risk stratification for individuals with such conditions are often based on analyses using the Cox proportional hazards model. This approach does not easily facilitate time-varying covariates and is often restricted to fixed time-point endpoint analyses such as time to first event analyses, rather than fully modelling all of the recurrent event process.  As such, many analyses are not utilising all available information, and predictions for an individual are made using baseline measurements rather than the latest recorded information.

Joint modelling of longitudinal and time-to-event data is a growing area of research. This methodology allows simultaneous analysis of some time-to-event outcome or outcomes, and one or more longitudinally (repeatedly measured over time) outcomes.  An example of longitudinal outcomes could be time-varying covariates or biomarkers updated at each medical appointment such as blood pressure or weight. The longitudinal and time-to-event components of the joint model are linked through some association structure, which represents the relationship between the longitudinal and time-to-event processes. 

Many joint modelling approaches have been proposed in the literature, however the majority assume a terminal event structure in the time to event component1, after which data for the individual is not utilised.  Additionally, many joint models restrict themselves to time-to-event approaches such as the Cox model, whose assumptions might not be valid in many clinical examples. Statistical approaches to model recurrent events are available include extensions to the Cox model, frailty models and multi-state models. However, these are rarely implemented within a joint modelling setting.

Before a model can be used in clinical practice to guide treatment choice and aid patient counselling, its performance must be assessed. Assessment should be made via evaluation of the models discrimination and calibration. These performance statistics are often omitted from publications. This may be due to complexities with outputting relevant data from existing code, or due to challenges with evaluating the model’s performance over time.

This project will therefore produce a framework for modelling longitudinal measured outcomes simultaneously with a recurrent event process to guide researchers to use the most appropriate methodology to maximise patient benefit. In particular, the objectives of this project are (i) to review use of methods for modelling recurrent events with time-varying covariates in joint models in the medical literature to gauge current uptake within chronic conditions research; (ii) to perform a simulation study to determine the most appropriate methods for modelling recurrent events with time-varying covariate measurements updated at regular intervals (iii) to design a guide to develop and validate models for recurrent event data and longitudinal outcomes from single studies including suggestions of appropriate software packages and data formats; (iv) to consider ways to present model outputs in a clinically meaningful and user-friendly way; (v) to apply the framework to clinical datasets available including epilepsy and asthma.